Variable Names

Looking at the data

There appears to be significant difference in the rate of bad variable naming between the low and high debt groups.

New Variable Names

d.both_completed %>%
  ggplot(aes(x=var_names_new_good.ratio, fill=high_debt_version)) + 
  geom_boxplot() +
  labs(
    title = "Distribution of good variable naming rate for the different debt levels (new variables)",
    x ="rate of good variable name selection"
  ) +
  scale_y_continuous(breaks = NULL) +
  scale_fill_manual(
    name = "Debt level", 
    labels = c("High debt", "Low debt"), 
    values = c("#7070FF", "lightblue"), 
    guide = guide_legend(reverse = TRUE)
  ) 

### Copied Variable Names

d.both_completed %>%
  ggplot(aes(x=var_names_copied_good.ratio, fill=high_debt_version)) + 
  geom_boxplot() +
  labs(
    title = "Distribution of good variable naming rate for the different debt levels (copied variables)",
    x ="rate of good variable name selection"
  ) +
  scale_y_continuous(breaks = NULL) +
  scale_fill_manual(
    name = "Debt level", 
    labels = c("High debt", "Low debt"), 
    values = c("#7070FF", "lightblue"), 
    guide = guide_legend(reverse = TRUE)
  ) 

## Warning: Removed 1 rows containing non-finite values (stat_boxplot).

Descriptive Statistics:

New Variable Names

d.both_completed %>%
  pull(var_names_new_good.ratio) %>% 
  summary()

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0000  1.0000  1.0000  0.8425  1.0000  1.0000

sprintf("Variance: %.2f", var(pull(d.both_completed, var_names_new_good.ratio)))

## [1] "Variance: 0.10"

Initial model

Variable names are modeled using the binomial family, where the amount of trials is the total amount of new variables..

We include high_debt_verison as well as a varying intercept for each individual in our initial model.

Selecting Priors

We iterate over the model until we have sane priors, in this case a prior giving a 50/50 chance was chosen in both cases. The prior “lkj(2)” will mean the model is sceptical of strong correlations.

Base model with priors

variable_names.with <- extendable_model(
  base_name = "variable_names",
  base_formula = "var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + (1  | session)",
  base_priors = c(
    prior(normal(0, 1), class = "b"),
    prior(normal(2, 1), class = "Intercept"),
    prior(exponential(1), class = "sd")
  ),
  family = binomial(),
  data = d.both_completed,
  base_control = list(adapt_delta = 0.95)
)

Default priors

prior_summary(variable_names.with(only_priors= TRUE))

Selected priors

prior_summary(variable_names.with(sample_prior = "only"))

Prior Predictive Check

pp_check(variable_names.with(sample_prior = "only"), nsamples = 200)

Beta Parameter Influence

Är detta verkligen rimligt öht?

sim.size <- 1000
sim.intercept <- rnorm(sim.size, 2, 1)
sim.beta <- rnorm(sim.size, 0, 1)
sim.beta.diff <- exp(sim.intercept + sim.beta) - exp(sim.intercept)

data.frame(x = sim.beta.diff) %>%
  ggplot(aes(x)) +
  geom_density() +
  xlim(-25, 25) +
  labs(
    title = "Beta parameter prior influence",
    x = "Good var names",
    y = "Density"
  )

Model fit

We check the posterior distribution and can see that the model seems to have been able to fit the data well Sampling seems to also have worked well as Rhat values are close to 1 and the sampling plots look nice. #### Posterior Predictive check

pp_check(variable_names.with(), nsamples = 200, type = "bars")

#### Summary

summary(variable_names.with())

##  Family: binomial 
##   Links: mu = logit 
## Formula: var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + (1 | session) 
##    Data: as.data.frame(data) (Number of observations: 44) 
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup samples = 4000
## 
## Group-Level Effects: 
## ~session (Number of levels: 22) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.73      0.60     0.73     3.13 1.00     1012     1849
## 
## Population-Level Effects: 
##                        Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                  1.49      0.50     0.62     2.59 1.00     2055
## high_debt_versionfalse     2.40      0.59     1.28     3.61 1.00     3646
##                        Tail_ESS
## Intercept                  2358
## high_debt_versionfalse     2980
## 
## Samples were drawn using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Sampling plots

plot(variable_names.with(), ask = FALSE)

Model predictor extenstions

# default prior for monotonic predictor
edlvl_prior <- prior(dirichlet(2), class = "simo", coef = "moeducation_level1")

One variable

loo_result <- loo(
  # Benchmark model(s)
  variable_names.with(),
  # New model(s)
  variable_names.with("work_domain"),
  variable_names.with("work_experience_programming.s"),
  variable_names.with("work_experience_java.s"),
  variable_names.with("education_field"),
  variable_names.with("mo(education_level)", edlvl_prior),
  variable_names.with("workplace_peer_review"),
  variable_names.with("workplace_td_tracking"),
  variable_names.with("workplace_pair_programming"),
  variable_names.with("workplace_coding_standards"),
  variable_names.with("scenario"),
  variable_names.with("group")
)

Comparison

loo_result[2]

## $diffs
##                                                         elpd_diff se_diff
## variable_names.with("scenario")                          0.0       0.0   
## variable_names.with("workplace_td_tracking")            -0.4       1.3   
## variable_names.with("education_field")                  -0.4       1.5   
## variable_names.with()                                   -0.5       1.2   
## variable_names.with("work_experience_java.s")           -0.7       1.1   
## variable_names.with("workplace_pair_programming")       -0.8       1.4   
## variable_names.with("group")                            -0.9       1.4   
## variable_names.with("work_domain")                      -1.1       1.3   
## variable_names.with("workplace_peer_review")            -1.1       1.1   
## variable_names.with("workplace_coding_standards")       -1.2       1.4   
## variable_names.with("work_experience_programming.s")    -1.3       1.1   
## variable_names.with("mo(education_level)", edlvl_prior) -1.8       1.5

Diagnostics

loo_result[1]

## $loos
## $loos$`variable_names.with()`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.3  6.1
## p_loo        14.6  2.8
## looic        72.6 12.1
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     21    47.7%   1443      
##  (0.5, 0.7]   (ok)       15    34.1%   165       
##    (0.7, 1]   (bad)       8    18.2%   81        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("work_domain")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.9  6.3
## p_loo        15.9  3.0
## looic        73.8 12.5
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     21    47.7%   1200      
##  (0.5, 0.7]   (ok)        9    20.5%   840       
##    (0.7, 1]   (bad)      14    31.8%   23        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("work_experience_programming.s")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -37.1  6.2
## p_loo        15.7  2.9
## looic        74.2 12.4
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     22    50.0%   1216      
##  (0.5, 0.7]   (ok)       11    25.0%   192       
##    (0.7, 1]   (bad)      10    22.7%   34        
##    (1, Inf)   (very bad)  1     2.3%   20        
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("work_experience_java.s")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.5  6.1
## p_loo        15.3  2.8
## looic        73.0 12.2
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     18    40.9%   1523      
##  (0.5, 0.7]   (ok)       16    36.4%   226       
##    (0.7, 1]   (bad)       9    20.5%   32        
##    (1, Inf)   (very bad)  1     2.3%   76        
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("education_field")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.2  6.0
## p_loo        13.2  2.5
## looic        72.4 12.0
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     24    54.5%   582       
##  (0.5, 0.7]   (ok)       12    27.3%   210       
##    (0.7, 1]   (bad)       8    18.2%   65        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("mo(education_level)", edlvl_prior)`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -37.5  6.5
## p_loo        16.1  3.2
## looic        75.1 12.9
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     20    45.5%   581       
##  (0.5, 0.7]   (ok)       12    27.3%   122       
##    (0.7, 1]   (bad)      11    25.0%   35        
##    (1, Inf)   (very bad)  1     2.3%   25        
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("workplace_peer_review")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.9  6.2
## p_loo        15.5  2.9
## looic        73.8 12.5
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     17    38.6%   1625      
##  (0.5, 0.7]   (ok)       15    34.1%   201       
##    (0.7, 1]   (bad)      12    27.3%   20        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("workplace_td_tracking")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.1  6.1
## p_loo        14.8  2.8
## looic        72.3 12.2
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     21    47.7%   1060      
##  (0.5, 0.7]   (ok)       13    29.5%   226       
##    (0.7, 1]   (bad)       9    20.5%   38        
##    (1, Inf)   (very bad)  1     2.3%   54        
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("workplace_pair_programming")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.5  6.2
## p_loo        15.2  2.9
## looic        73.1 12.3
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     18    40.9%   1484      
##  (0.5, 0.7]   (ok)       15    34.1%   251       
##    (0.7, 1]   (bad)      11    25.0%   68        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("workplace_coding_standards")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -37.0  6.3
## p_loo        15.7  3.1
## looic        74.0 12.6
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     25    56.8%   1315      
##  (0.5, 0.7]   (ok)       10    22.7%   105       
##    (0.7, 1]   (bad)       8    18.2%   45        
##    (1, Inf)   (very bad)  1     2.3%   10        
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("scenario")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -35.8  5.8
## p_loo        14.7  2.6
## looic        71.5 11.7
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     20    45.5%   1434      
##  (0.5, 0.7]   (ok)       13    29.5%   243       
##    (0.7, 1]   (bad)      11    25.0%   47        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("group")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.7  6.2
## p_loo        15.6  3.0
## looic        73.3 12.4
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     22    50.0%   2053      
##  (0.5, 0.7]   (ok)       12    27.3%   168       
##    (0.7, 1]   (bad)       9    20.5%   57        
##    (1, Inf)   (very bad)  1     2.3%   33        
## See help('pareto-k-diagnostic') for details.

Two variables

loo_result <- loo(
  # Benchmark model(s)
  variable_names.with(),
  variable_names.with("work_experience_programming.s"),
  variable_names.with("work_experience_java.s"),
  variable_names.with("workplace_peer_review"),
  variable_names.with("workplace_td_tracking"),
  variable_names.with("workplace_coding_standards"),
  #New model(s)
  variable_names.with(c("scenario","workplace_td_tracking")),
  variable_names.with(c("scenario","workplace_peer_review")),
  variable_names.with(c("scenario","work_experience_java.s"))
)

Comparison

loo_result[2]

## $diffs
##                                                              elpd_diff se_diff
## variable_names.with(c("scenario", "workplace_peer_review"))   0.0       0.0   
## variable_names.with("workplace_td_tracking")                 -0.1       1.5   
## variable_names.with()                                        -0.3       1.4   
## variable_names.with("work_experience_java.s")                -0.5       1.3   
## variable_names.with(c("scenario", "work_experience_java.s")) -0.6       0.6   
## variable_names.with(c("scenario", "workplace_td_tracking"))  -0.7       0.8   
## variable_names.with("workplace_peer_review")                 -0.9       1.2   
## variable_names.with("workplace_coding_standards")            -1.0       1.4   
## variable_names.with("work_experience_programming.s")         -1.1       1.2

Diagnostics

loo_result[1]

## $loos
## $loos$`variable_names.with()`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.3  6.1
## p_loo        14.6  2.8
## looic        72.6 12.1
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     21    47.7%   1443      
##  (0.5, 0.7]   (ok)       15    34.1%   165       
##    (0.7, 1]   (bad)       8    18.2%   81        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("work_experience_programming.s")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -37.1  6.2
## p_loo        15.7  2.9
## looic        74.2 12.4
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     22    50.0%   1216      
##  (0.5, 0.7]   (ok)       11    25.0%   192       
##    (0.7, 1]   (bad)      10    22.7%   34        
##    (1, Inf)   (very bad)  1     2.3%   20        
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("work_experience_java.s")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.5  6.1
## p_loo        15.3  2.8
## looic        73.0 12.2
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     18    40.9%   1523      
##  (0.5, 0.7]   (ok)       16    36.4%   226       
##    (0.7, 1]   (bad)       9    20.5%   32        
##    (1, Inf)   (very bad)  1     2.3%   76        
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("workplace_peer_review")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.9  6.2
## p_loo        15.5  2.9
## looic        73.8 12.5
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     17    38.6%   1625      
##  (0.5, 0.7]   (ok)       15    34.1%   201       
##    (0.7, 1]   (bad)      12    27.3%   20        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("workplace_td_tracking")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.1  6.1
## p_loo        14.8  2.8
## looic        72.3 12.2
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     21    47.7%   1060      
##  (0.5, 0.7]   (ok)       13    29.5%   226       
##    (0.7, 1]   (bad)       9    20.5%   38        
##    (1, Inf)   (very bad)  1     2.3%   54        
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("workplace_coding_standards")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -37.0  6.3
## p_loo        15.7  3.1
## looic        74.0 12.6
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     25    56.8%   1315      
##  (0.5, 0.7]   (ok)       10    22.7%   105       
##    (0.7, 1]   (bad)       8    18.2%   45        
##    (1, Inf)   (very bad)  1     2.3%   10        
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with(c("scenario", "workplace_td_tracking"))`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.7  6.0
## p_loo        15.7  2.8
## looic        73.3 12.0
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     22    50.0%   889       
##  (0.5, 0.7]   (ok)        6    13.6%   535       
##    (0.7, 1]   (bad)      16    36.4%   37        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with(c("scenario", "workplace_peer_review"))`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.0  6.0
## p_loo        15.2  2.8
## looic        72.0 11.9
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     18    40.9%   1509      
##  (0.5, 0.7]   (ok)       16    36.4%   177       
##    (0.7, 1]   (bad)      10    22.7%   30        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with(c("scenario", "work_experience_java.s"))`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.6  6.0
## p_loo        15.8  2.9
## looic        73.1 12.0
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     17    38.6%   1592      
##  (0.5, 0.7]   (ok)       14    31.8%   775       
##    (0.7, 1]   (bad)      13    29.5%   58        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.

Three variables

loo(
  # Benchmark model(s)
  variable_names.with(),
  variable_names.with("work_experience_programming.s"),
  variable_names.with("work_experience_java.s"),
  variable_names.with("workplace_peer_review"),
  variable_names.with("workplace_td_tracking"),
  variable_names.with("workplace_coding_standards"),
  variable_names.with(c("scenario","workplace_td_tracking")),
  variable_names.with(c("scenario","workplace_peer_review")),
  # New model(s)
  variable_names.with(c("scenario","work_experience_java.s")),
  variable_names.with(c("scenario","work_experience_java.s","workplace_td_tracking","workplace_peer_review")),
  variable_names.with(c("scenario","work_experience_java.s","workplace_td_tracking"))
)

## Output of model 'variable_names.with()':
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.3  6.1
## p_loo        14.6  2.8
## looic        72.6 12.1
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     21    47.7%   1443      
##  (0.5, 0.7]   (ok)       15    34.1%   165       
##    (0.7, 1]   (bad)       8    18.2%   81        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## Output of model 'variable_names.with("work_experience_programming.s")':
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -37.1  6.2
## p_loo        15.7  2.9
## looic        74.2 12.4
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     22    50.0%   1216      
##  (0.5, 0.7]   (ok)       11    25.0%   192       
##    (0.7, 1]   (bad)      10    22.7%   34        
##    (1, Inf)   (very bad)  1     2.3%   20        
## See help('pareto-k-diagnostic') for details.
## 
## Output of model 'variable_names.with("work_experience_java.s")':
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.5  6.1
## p_loo        15.3  2.8
## looic        73.0 12.2
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     18    40.9%   1523      
##  (0.5, 0.7]   (ok)       16    36.4%   226       
##    (0.7, 1]   (bad)       9    20.5%   32        
##    (1, Inf)   (very bad)  1     2.3%   76        
## See help('pareto-k-diagnostic') for details.
## 
## Output of model 'variable_names.with("workplace_peer_review")':
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.9  6.2
## p_loo        15.5  2.9
## looic        73.8 12.5
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     17    38.6%   1625      
##  (0.5, 0.7]   (ok)       15    34.1%   201       
##    (0.7, 1]   (bad)      12    27.3%   20        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## Output of model 'variable_names.with("workplace_td_tracking")':
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.1  6.1
## p_loo        14.8  2.8
## looic        72.3 12.2
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     21    47.7%   1060      
##  (0.5, 0.7]   (ok)       13    29.5%   226       
##    (0.7, 1]   (bad)       9    20.5%   38        
##    (1, Inf)   (very bad)  1     2.3%   54        
## See help('pareto-k-diagnostic') for details.
## 
## Output of model 'variable_names.with("workplace_coding_standards")':
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -37.0  6.3
## p_loo        15.7  3.1
## looic        74.0 12.6
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     25    56.8%   1315      
##  (0.5, 0.7]   (ok)       10    22.7%   105       
##    (0.7, 1]   (bad)       8    18.2%   45        
##    (1, Inf)   (very bad)  1     2.3%   10        
## See help('pareto-k-diagnostic') for details.
## 
## Output of model 'variable_names.with(c("scenario", "workplace_td_tracking"))':
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.7  6.0
## p_loo        15.7  2.8
## looic        73.3 12.0
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     22    50.0%   889       
##  (0.5, 0.7]   (ok)        6    13.6%   535       
##    (0.7, 1]   (bad)      16    36.4%   37        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## Output of model 'variable_names.with(c("scenario", "workplace_peer_review"))':
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.0  6.0
## p_loo        15.2  2.8
## looic        72.0 11.9
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     18    40.9%   1509      
##  (0.5, 0.7]   (ok)       16    36.4%   177       
##    (0.7, 1]   (bad)      10    22.7%   30        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## Output of model 'variable_names.with(c("scenario", "work_experience_java.s"))':
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.6  6.0
## p_loo        15.8  2.9
## looic        73.1 12.0
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     17    38.6%   1592      
##  (0.5, 0.7]   (ok)       14    31.8%   775       
##    (0.7, 1]   (bad)      13    29.5%   58        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## Output of model 'variable_names.with(c("scenario", "work_experience_java.s", "workplace_td_tracking",     "workplace_peer_review"))':
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.9  6.2
## p_loo        16.5  3.1
## looic        73.7 12.4
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     22    50.0%   764       
##  (0.5, 0.7]   (ok)        9    20.5%   212       
##    (0.7, 1]   (bad)      11    25.0%   25        
##    (1, Inf)   (very bad)  2     4.5%   20        
## See help('pareto-k-diagnostic') for details.
## 
## Output of model 'variable_names.with(c("scenario", "work_experience_java.s", "workplace_td_tracking"))':
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.7  6.1
## p_loo        16.0  2.9
## looic        73.4 12.1
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     23    52.3%   891       
##  (0.5, 0.7]   (ok)       11    25.0%   319       
##    (0.7, 1]   (bad)       9    20.5%   38        
##    (1, Inf)   (very bad)  1     2.3%   18        
## See help('pareto-k-diagnostic') for details.
## 
## Model comparisons:
##                                                                                                                    elpd_diff
## variable_names.with(c("scenario", "workplace_peer_review"))                                                         0.0     
## variable_names.with("workplace_td_tracking")                                                                       -0.1     
## variable_names.with()                                                                                              -0.3     
## variable_names.with("work_experience_java.s")                                                                      -0.5     
## variable_names.with(c("scenario", "work_experience_java.s"))                                                       -0.6     
## variable_names.with(c("scenario", "workplace_td_tracking"))                                                        -0.7     
## variable_names.with(c("scenario", "work_experience_java.s", "workplace_td_tracking"))                              -0.7     
## variable_names.with(c("scenario", "work_experience_java.s", "workplace_td_tracking",     "workplace_peer_review")) -0.9     
## variable_names.with("workplace_peer_review")                                                                       -0.9     
## variable_names.with("workplace_coding_standards")                                                                  -1.0     
## variable_names.with("work_experience_programming.s")                                                               -1.1     
##                                                                                                                    se_diff
## variable_names.with(c("scenario", "workplace_peer_review"))                                                         0.0   
## variable_names.with("workplace_td_tracking")                                                                        1.5   
## variable_names.with()                                                                                               1.4   
## variable_names.with("work_experience_java.s")                                                                       1.3   
## variable_names.with(c("scenario", "work_experience_java.s"))                                                        0.6   
## variable_names.with(c("scenario", "workplace_td_tracking"))                                                         0.8   
## variable_names.with(c("scenario", "work_experience_java.s", "workplace_td_tracking"))                               0.8   
## variable_names.with(c("scenario", "work_experience_java.s", "workplace_td_tracking",     "workplace_peer_review"))  0.8   
## variable_names.with("workplace_peer_review")                                                                        1.2   
## variable_names.with("workplace_coding_standards")                                                                   1.4   
## variable_names.with("work_experience_programming.s")                                                                1.2

Comparison

loo_result[2]

## $diffs
##                                                              elpd_diff se_diff
## variable_names.with(c("scenario", "workplace_peer_review"))   0.0       0.0   
## variable_names.with("workplace_td_tracking")                 -0.1       1.5   
## variable_names.with()                                        -0.3       1.4   
## variable_names.with("work_experience_java.s")                -0.5       1.3   
## variable_names.with(c("scenario", "work_experience_java.s")) -0.6       0.6   
## variable_names.with(c("scenario", "workplace_td_tracking"))  -0.7       0.8   
## variable_names.with("workplace_peer_review")                 -0.9       1.2   
## variable_names.with("workplace_coding_standards")            -1.0       1.4   
## variable_names.with("work_experience_programming.s")         -1.1       1.2

Diagnostics

loo_result[1]

## $loos
## $loos$`variable_names.with()`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.3  6.1
## p_loo        14.6  2.8
## looic        72.6 12.1
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     21    47.7%   1443      
##  (0.5, 0.7]   (ok)       15    34.1%   165       
##    (0.7, 1]   (bad)       8    18.2%   81        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("work_experience_programming.s")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -37.1  6.2
## p_loo        15.7  2.9
## looic        74.2 12.4
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     22    50.0%   1216      
##  (0.5, 0.7]   (ok)       11    25.0%   192       
##    (0.7, 1]   (bad)      10    22.7%   34        
##    (1, Inf)   (very bad)  1     2.3%   20        
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("work_experience_java.s")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.5  6.1
## p_loo        15.3  2.8
## looic        73.0 12.2
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     18    40.9%   1523      
##  (0.5, 0.7]   (ok)       16    36.4%   226       
##    (0.7, 1]   (bad)       9    20.5%   32        
##    (1, Inf)   (very bad)  1     2.3%   76        
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("workplace_peer_review")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.9  6.2
## p_loo        15.5  2.9
## looic        73.8 12.5
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     17    38.6%   1625      
##  (0.5, 0.7]   (ok)       15    34.1%   201       
##    (0.7, 1]   (bad)      12    27.3%   20        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("workplace_td_tracking")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.1  6.1
## p_loo        14.8  2.8
## looic        72.3 12.2
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     21    47.7%   1060      
##  (0.5, 0.7]   (ok)       13    29.5%   226       
##    (0.7, 1]   (bad)       9    20.5%   38        
##    (1, Inf)   (very bad)  1     2.3%   54        
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with("workplace_coding_standards")`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -37.0  6.3
## p_loo        15.7  3.1
## looic        74.0 12.6
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     25    56.8%   1315      
##  (0.5, 0.7]   (ok)       10    22.7%   105       
##    (0.7, 1]   (bad)       8    18.2%   45        
##    (1, Inf)   (very bad)  1     2.3%   10        
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with(c("scenario", "workplace_td_tracking"))`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.7  6.0
## p_loo        15.7  2.8
## looic        73.3 12.0
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     22    50.0%   889       
##  (0.5, 0.7]   (ok)        6    13.6%   535       
##    (0.7, 1]   (bad)      16    36.4%   37        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with(c("scenario", "workplace_peer_review"))`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.0  6.0
## p_loo        15.2  2.8
## looic        72.0 11.9
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     18    40.9%   1509      
##  (0.5, 0.7]   (ok)       16    36.4%   177       
##    (0.7, 1]   (bad)      10    22.7%   30        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## $loos$`variable_names.with(c("scenario", "work_experience_java.s"))`
## 
## Computed from 4000 by 44 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -36.6  6.0
## p_loo        15.8  2.9
## looic        73.1 12.0
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     17    38.6%   1592      
##  (0.5, 0.7]   (ok)       14    31.8%   775       
##    (0.7, 1]   (bad)      13    29.5%   58        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.

Candidate models

We pick some of our top performing models as candidates and inspect them closer.

The candidate models are named and listed in order of complexity.

variable_names0

We select the simplest model as a baseline.

variable_names0 <- brm(
  "var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + (1 | session)",
  prior = c(
    prior(normal(0, 1), class = "b"),
    prior(normal(2, 1), class = "Intercept"),
    prior(exponential(1), class = "sd")
  ),
  family = binomial(),
  data = d.both_completed,
  control = list(adapt_delta = 0.95),
  file = "fits/variable_names0",
  file_refit = "on_change",
  seed = 20210421
)

Summary

summary(variable_names0)

##  Family: binomial 
##   Links: mu = logit 
## Formula: var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + (1 | session) 
##    Data: d.both_completed (Number of observations: 44) 
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup samples = 4000
## 
## Group-Level Effects: 
## ~session (Number of levels: 22) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.73      0.60     0.73     3.13 1.00     1012     1849
## 
## Population-Level Effects: 
##                        Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                  1.49      0.50     0.62     2.59 1.00     2055
## high_debt_versionfalse     2.40      0.59     1.28     3.61 1.00     3646
##                        Tail_ESS
## Intercept                  2358
## high_debt_versionfalse     2980
## 
## Samples were drawn using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Random effects

ranef(variable_names0)

## $session
## , , Intercept
## 
##                            Estimate Est.Error       Q2.5       Q97.5
## 6033d69a5af2c702367b3a95  0.9593728 1.4598093 -1.4266878  4.35681025
## 6033d90a5af2c702367b3a96  1.2230461 1.3741480 -1.0700565  4.34180050
## 6034fc165af2c702367b3a98 -1.3461432 0.6400501 -2.6174202 -0.14643655
## 603500725af2c702367b3a99 -1.4742955 1.0719886 -3.6895763  0.53541888
## 603f97625af2c702367b3a9d  1.2794403 1.4101163 -0.9540715  4.59459200
## 603fd5d95af2c702367b3a9e -1.4598097 1.0828863 -3.6483898  0.62073472
## 60409b7b5af2c702367b3a9f  1.2307225 1.4401095 -1.0276302  4.64772975
## 604b82b5a7718fbed181b336 -0.8433473 0.8443749 -2.5238425  0.75539888
## 6050c1bf856f36729d2e5218 -1.8230547 1.0291442 -3.9423910  0.05089144
## 6050e1e7856f36729d2e5219  1.2152962 1.3938698 -1.0467375  4.47374750
## 6055fdc6856f36729d2e521b  0.9924102 1.4850145 -1.4927917  4.32935150
## 60589862856f36729d2e521f  1.0562901 1.5039300 -1.4083792  4.56801325
## 605afa3a856f36729d2e5222 -1.5634428 1.1462360 -3.8976315  0.50356810
## 605c8bc6856f36729d2e5223 -0.9095465 0.9745567 -2.8730900  0.95339948
## 605f3f2d856f36729d2e5224  0.9674901 1.4864794 -1.4442637  4.38204675
## 605f46c3856f36729d2e5225 -1.6011170 0.8800919 -3.4298875  0.05894927
## 60605337856f36729d2e5226  0.9504888 1.4504408 -1.4196987  4.34745700
## 60609ae6856f36729d2e5228  1.2287439 1.3950698 -0.9455645  4.55586525
## 6061ce91856f36729d2e522e  1.2291203 1.4048307 -1.0173040  4.51340125
## 6061f106856f36729d2e5231 -1.4715682 1.0739459 -3.6457168  0.59643020
## 6068ea9f856f36729d2e523e  1.5684952 1.3439166 -0.4693869  4.83278950
## 6075ab05856f36729d2e5247  1.2781836 1.4038392 -0.9955097  4.59275500

Sampling plots

plot(variable_names0, ask = FALSE)

Posterior predictive check

pp_check(variable_names0, nsamples = 200, type = "bars") 

variable_names1

We select the best performing model with one variable.

variable_names1 <- brm(
  "var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + scenario + (1 | session)",
  prior = c(
    prior(normal(0, 1), class = "b"),
    prior(normal(2, 1), class = "Intercept"),
    prior(exponential(1), class = "sd")
  ),
  family = binomial(),
  data = d.both_completed,
  control = list(adapt_delta = 0.95),
  file = "fits/variable_names1",
  file_refit = "on_change",
  seed = 20210421
)

Summary

summary(variable_names1)

##  Family: binomial 
##   Links: mu = logit 
## Formula: var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + scenario + (1 | session) 
##    Data: d.both_completed (Number of observations: 44) 
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup samples = 4000
## 
## Group-Level Effects: 
## ~session (Number of levels: 22) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.78      0.63     0.74     3.20 1.00     1475     2333
## 
## Population-Level Effects: 
##                        Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                  1.74      0.55     0.77     2.94 1.00     2253
## high_debt_versionfalse     2.42      0.56     1.34     3.57 1.00     4049
## scenariotickets           -0.64      0.53    -1.69     0.38 1.00     4095
##                        Tail_ESS
## Intercept                  2734
## high_debt_versionfalse     2752
## scenariotickets            2543
## 
## Samples were drawn using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Random effects

ranef(variable_names1)

## $session
## , , Intercept
## 
##                           Estimate Est.Error       Q2.5       Q97.5
## 6033d69a5af2c702367b3a95  1.093066 1.4632462 -1.3590025  4.41794275
## 6033d90a5af2c702367b3a96  1.199225 1.4948853 -1.1250630  4.53985300
## 6034fc165af2c702367b3a98 -1.570729 0.6830682 -3.0035820 -0.33337780
## 603500725af2c702367b3a99 -1.409009 1.1044456 -3.6444140  0.66224548
## 603f97625af2c702367b3a9d  1.248668 1.4289584 -1.0143170  4.49822175
## 603fd5d95af2c702367b3a9e -1.444694 1.1540950 -3.8164280  0.72340865
## 60409b7b5af2c702367b3a9f  1.193507 1.4823702 -1.0945442  4.71445900
## 604b82b5a7718fbed181b336 -1.025820 0.8695539 -2.8164268  0.60527305
## 6050c1bf856f36729d2e5218 -1.760403 1.0587253 -3.9362907  0.20798768
## 6050e1e7856f36729d2e5219  1.235263 1.4966840 -1.1258432  4.71174075
## 6055fdc6856f36729d2e521b  1.127720 1.4940310 -1.3266358  4.66202900
## 60589862856f36729d2e521f  1.162000 1.4871669 -1.2509405  4.72933225
## 605afa3a856f36729d2e5222 -1.517017 1.1826029 -3.9205807  0.73074608
## 605c8bc6856f36729d2e5223 -1.027399 0.9818350 -3.0101878  0.83709883
## 605f3f2d856f36729d2e5224  1.127413 1.4812606 -1.2892175  4.65922200
## 605f46c3856f36729d2e5225 -1.726124 0.8997469 -3.5510050 -0.05501024
## 60605337856f36729d2e5226  1.123126 1.4774671 -1.3124718  4.61499750
## 60609ae6856f36729d2e5228  1.225445 1.4894106 -1.1406840  4.75353650
## 6061ce91856f36729d2e522e  1.215768 1.4866867 -1.1666405  4.67304150
## 6061f106856f36729d2e5231 -1.431271 1.0992919 -3.6732065  0.62742388
## 6068ea9f856f36729d2e523e  1.606133 1.3889929 -0.5727873  4.87182500
## 6075ab05856f36729d2e5247  1.193832 1.4749458 -1.1719053  4.61740875

Sampling plots

plot(variable_names1, ask = FALSE)

Posterior predictive check

pp_check(variable_names1, nsamples = 200, type = "bars")

variable_names2

We select the best performing model with one variable.

variable_names2 <- brm(
  "var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + scenario + work_experience_java.s + (1 | session)",
  prior = c(
    prior(normal(0, 1), class = "b"),
    prior(normal(2, 1), class = "Intercept"),
    prior(exponential(1), class = "sd")
  ),
  family = binomial(),
  data = d.both_completed,
  control = list(adapt_delta = 0.95),
  file = "fits/variable_names2",
  file_refit = "on_change",
  seed = 20210421
)

Summary

summary(variable_names2)

##  Family: binomial 
##   Links: mu = logit 
## Formula: var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + scenario + work_experience_java.s + (1 | session) 
##    Data: d.both_completed (Number of observations: 44) 
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup samples = 4000
## 
## Group-Level Effects: 
## ~session (Number of levels: 22) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.87      0.65     0.84     3.38 1.00     1156     2050
## 
## Population-Level Effects: 
##                        Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                  1.81      0.57     0.79     3.00 1.00     2223
## high_debt_versionfalse     2.42      0.56     1.33     3.56 1.00     3898
## scenariotickets           -0.68      0.54    -1.75     0.38 1.00     4098
## work_experience_java.s     0.19      0.52    -0.83     1.25 1.00     2292
##                        Tail_ESS
## Intercept                  2688
## high_debt_versionfalse     2983
## scenariotickets            2827
## work_experience_java.s     2695
## 
## Samples were drawn using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Random effects

ranef(variable_names2)

## $session
## , , Intercept
## 
##                           Estimate Est.Error       Q2.5        Q97.5
## 6033d69a5af2c702367b3a95  1.255241 1.6053544 -1.3900780  5.159761750
## 6033d90a5af2c702367b3a96  1.294544 1.5418674 -1.2093457  4.782044750
## 6034fc165af2c702367b3a98 -1.556082 0.7137566 -2.9827595 -0.221446625
## 603500725af2c702367b3a99 -1.430599 1.1381464 -3.7108325  0.695586375
## 603f97625af2c702367b3a9d  1.369281 1.4948888 -1.0121733  4.841596000
## 603fd5d95af2c702367b3a9e -1.404366 1.1495959 -3.7413395  0.733319100
## 60409b7b5af2c702367b3a9f  1.296609 1.5265936 -1.1419105  4.965830250
## 604b82b5a7718fbed181b336 -1.030896 0.8844133 -2.7825160  0.656808625
## 6050c1bf856f36729d2e5218 -1.795700 1.0990693 -4.0444755  0.250461950
## 6050e1e7856f36729d2e5219  1.282235 1.5265490 -1.1986235  4.830863000
## 6055fdc6856f36729d2e521b  1.226939 1.5587861 -1.2501895  4.858555500
## 60589862856f36729d2e521f  1.124807 1.5741603 -1.5739028  4.689689000
## 605afa3a856f36729d2e5222 -1.779118 1.3643354 -4.6536703  0.687837200
## 605c8bc6856f36729d2e5223 -1.191728 1.0574864 -3.2684370  0.881749075
## 605f3f2d856f36729d2e5224  1.057338 1.8417415 -2.1496275  5.221295000
## 605f46c3856f36729d2e5225 -1.748655 0.9338799 -3.6239415  0.002337589
## 60605337856f36729d2e5226  1.209346 1.6016507 -1.3611807  4.915383750
## 60609ae6856f36729d2e5228  1.286541 1.5000872 -1.1147158  4.710303500
## 6061ce91856f36729d2e522e  1.296802 1.5222352 -1.1925990  4.764905750
## 6061f106856f36729d2e5231 -1.414230 1.1667625 -3.8232542  0.782362025
## 6068ea9f856f36729d2e523e  1.662751 1.4977089 -0.6433186  5.295703000
## 6075ab05856f36729d2e5247  1.305361 1.5232928 -1.1335567  4.860366750

Sampling plots

plot(variable_names2, ask = FALSE)

Posterior predictive check

pp_check(variable_names2, nsamples = 200, type = "bars")

variable_names3

We select the best performing model with one variable.

variable_names3 <- brm(
  "var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + scenario + work_experience_java.s + (1 | session)",
  prior = c(
    prior(normal(0, 1), class = "b"),
    prior(normal(2, 1), class = "Intercept"),
    prior(exponential(1), class = "sd")
  ),
  family = binomial(),
  data = d.both_completed,
  control = list(adapt_delta = 0.95),
  file = "fits/variable_names3",
  file_refit = "on_change",
  seed = 20210421
)

Summary

summary(variable_names3)

##  Family: binomial 
##   Links: mu = logit 
## Formula: var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + scenario + work_experience_java.s + (1 | session) 
##    Data: d.both_completed (Number of observations: 44) 
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup samples = 4000
## 
## Group-Level Effects: 
## ~session (Number of levels: 22) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.87      0.65     0.84     3.38 1.00     1156     2050
## 
## Population-Level Effects: 
##                        Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                  1.81      0.57     0.79     3.00 1.00     2223
## high_debt_versionfalse     2.42      0.56     1.33     3.56 1.00     3898
## scenariotickets           -0.68      0.54    -1.75     0.38 1.00     4098
## work_experience_java.s     0.19      0.52    -0.83     1.25 1.00     2292
##                        Tail_ESS
## Intercept                  2688
## high_debt_versionfalse     2983
## scenariotickets            2827
## work_experience_java.s     2695
## 
## Samples were drawn using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Random effects

ranef(variable_names3)

## $session
## , , Intercept
## 
##                           Estimate Est.Error       Q2.5        Q97.5
## 6033d69a5af2c702367b3a95  1.255241 1.6053544 -1.3900780  5.159761750
## 6033d90a5af2c702367b3a96  1.294544 1.5418674 -1.2093457  4.782044750
## 6034fc165af2c702367b3a98 -1.556082 0.7137566 -2.9827595 -0.221446625
## 603500725af2c702367b3a99 -1.430599 1.1381464 -3.7108325  0.695586375
## 603f97625af2c702367b3a9d  1.369281 1.4948888 -1.0121733  4.841596000
## 603fd5d95af2c702367b3a9e -1.404366 1.1495959 -3.7413395  0.733319100
## 60409b7b5af2c702367b3a9f  1.296609 1.5265936 -1.1419105  4.965830250
## 604b82b5a7718fbed181b336 -1.030896 0.8844133 -2.7825160  0.656808625
## 6050c1bf856f36729d2e5218 -1.795700 1.0990693 -4.0444755  0.250461950
## 6050e1e7856f36729d2e5219  1.282235 1.5265490 -1.1986235  4.830863000
## 6055fdc6856f36729d2e521b  1.226939 1.5587861 -1.2501895  4.858555500
## 60589862856f36729d2e521f  1.124807 1.5741603 -1.5739028  4.689689000
## 605afa3a856f36729d2e5222 -1.779118 1.3643354 -4.6536703  0.687837200
## 605c8bc6856f36729d2e5223 -1.191728 1.0574864 -3.2684370  0.881749075
## 605f3f2d856f36729d2e5224  1.057338 1.8417415 -2.1496275  5.221295000
## 605f46c3856f36729d2e5225 -1.748655 0.9338799 -3.6239415  0.002337589
## 60605337856f36729d2e5226  1.209346 1.6016507 -1.3611807  4.915383750
## 60609ae6856f36729d2e5228  1.286541 1.5000872 -1.1147158  4.710303500
## 6061ce91856f36729d2e522e  1.296802 1.5222352 -1.1925990  4.764905750
## 6061f106856f36729d2e5231 -1.414230 1.1667625 -3.8232542  0.782362025
## 6068ea9f856f36729d2e523e  1.662751 1.4977089 -0.6433186  5.295703000
## 6075ab05856f36729d2e5247  1.305361 1.5232928 -1.1335567  4.860366750

Sampling plots

plot(variable_names3, ask = FALSE)

Posterior predictive check

pp_check(variable_names2, nsamples = 200, type = "bars")

Final Model

All candidate models look nice, none is significantly better than the others, we will proceed the simplest model: variable_names0

Variations

We will try a few different variations of the selected candidate model.

All data points

Some participants only completed one scenario. Those has been excluded from the initial dataset to improve sampling of the models. We do however want to use all data we can and will therefore try to fit the model with the complete dataset.

Some participants only completed one scenario. Those has been excluded from the initial dataset to improve sampling of the models. We do however want to use all data we can and will therefore try to fit the model with the complete dataset.

variable_names0.all <- brm(
  "var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + (1 | session)",
  prior = c(
    prior(normal(0, 1), class = "b"),
    prior(normal(2, 1), class = "Intercept"),
    prior(exponential(1), class = "sd")
  ),
  family = binomial(),
  data = as.data.frame(d.completed),
  control = list(adapt_delta = 0.95),
  file = "fits/variable_names0.all",
  file_refit = "on_change",
seed = 20210421
)

Summary

summary(variable_names0.all)

##  Family: binomial 
##   Links: mu = logit 
## Formula: var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + (1 | session) 
##    Data: as.data.frame(d.completed) (Number of observations: 51) 
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup samples = 4000
## 
## Group-Level Effects: 
## ~session (Number of levels: 29) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.68      0.56     0.73     2.88 1.00     1366     1947
## 
## Population-Level Effects: 
##                        Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                  1.48      0.47     0.64     2.48 1.00     2471
## high_debt_versionfalse     2.48      0.56     1.38     3.63 1.00     4459
##                        Tail_ESS
## Intercept                  2924
## high_debt_versionfalse     3101
## 
## Samples were drawn using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Random effects

ranef(variable_names0.all)

## $session
## , , Intercept
## 
##                            Estimate Est.Error       Q2.5        Q97.5
## 6033c6fc5af2c702367b3a93 -1.3869510 1.1083804 -3.8059562  0.640411375
## 6033d69a5af2c702367b3a95  0.9464261 1.4285258 -1.3969613  4.269342250
## 6033d90a5af2c702367b3a96  1.2207704 1.4042311 -1.0971247  4.478865000
## 6034fc165af2c702367b3a98 -1.3309234 0.6231877 -2.5818770 -0.161306950
## 603500725af2c702367b3a99 -1.4661002 1.0549079 -3.6853402  0.487411200
## 603f84f15af2c702367b3a9b  0.2402520 1.6041079 -2.6659903  3.716927500
## 603f97625af2c702367b3a9d  1.2332757 1.3681069 -0.9525377  4.445348250
## 603fd5d95af2c702367b3a9e -1.4621612 1.0503431 -3.6188418  0.455923700
## 60409b7b5af2c702367b3a9f  1.1755969 1.3813356 -1.0581940  4.415432500
## 604b82b5a7718fbed181b336 -0.8481773 0.8143013 -2.4817405  0.734885900
## 604f1239a7718fbed181b33f  0.8292040 1.4489824 -1.6342780  4.167540750
## 6050c1bf856f36729d2e5218 -1.8170189 0.9803604 -3.8701228  0.001106741
## 6050e1e7856f36729d2e5219  1.2178405 1.3740012 -1.0049792  4.283213500
## 6055fdc6856f36729d2e521b  0.9593235 1.3948570 -1.3593255  4.085696000
## 60579f2a856f36729d2e521e  0.2664243 1.6512415 -2.8754408  3.754241250
## 60589862856f36729d2e521f  0.9479557 1.3618734 -1.2958543  4.018388750
## 605a30a7856f36729d2e5221  0.1532920 1.7078751 -3.1326363  3.890949750
## 605afa3a856f36729d2e5222 -1.5711265 1.0827390 -3.8075067  0.384341750
## 605c8bc6856f36729d2e5223 -0.8891101 0.9675897 -2.7592045  0.983294425
## 605f3f2d856f36729d2e5224  0.9129801 1.4034211 -1.4173490  4.173405250
## 605f46c3856f36729d2e5225 -1.5649874 0.8896083 -3.4256675  0.028091653
## 60605337856f36729d2e5226  0.9038988 1.3661650 -1.3900227  4.107031500
## 60609ae6856f36729d2e5228  1.2167153 1.3845780 -0.9594529  4.446352750
## 6061ce91856f36729d2e522e  1.2286107 1.3928314 -1.0167965  4.369936750
## 6061f106856f36729d2e5231 -1.4675347 1.0699160 -3.6145143  0.529039150
## 60672faa856f36729d2e523c  0.2738112 1.5961321 -2.5484403  3.872159750
## 6068ea9f856f36729d2e523e  1.5420235 1.3225310 -0.5237006  4.541578250
## 606db69d856f36729d2e5243  0.4964141 1.5464307 -2.2223970  3.969827250
## 6075ab05856f36729d2e5247  1.1906455 1.3682642 -1.0126700  4.445376000

Sampling plots

plot(variable_names0.all, ask = FALSE)

Posterior predictive check

pp_check(variable_names0.all, nsamples = 200, type = "bars")

With experience predictor

As including all data points didn’t harm the model we will create this variant with all data points as well.

This variation includes work_experience_programming.s predictors as it can give further insight into how experience play a factor in the effect we try to measure. This is especially important as our sampling shewed towards containing less experienced developer than the population at large.

variable_names0.all.exp <- brm(
  "var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + work_experience_programming.s + (1 | session)",
  prior = c(
    prior(normal(0, 1), class = "b"),
    prior(normal(2, 1), class = "Intercept"),
    prior(exponential(1), class = "sd")
  ),
  family = binomial(),
  data = as.data.frame(d.completed),
  control = list(adapt_delta = 0.95),
  file = "fits/variable_names0.all.exp",
  file_refit = "on_change",
  seed = 20210421
)

summary(variable_names0.all)

##  Family: binomial 
##   Links: mu = logit 
## Formula: var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + (1 | session) 
##    Data: as.data.frame(d.completed) (Number of observations: 51) 
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup samples = 4000
## 
## Group-Level Effects: 
## ~session (Number of levels: 29) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.68      0.56     0.73     2.88 1.00     1366     1947
## 
## Population-Level Effects: 
##                        Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                  1.48      0.47     0.64     2.48 1.00     2471
## high_debt_versionfalse     2.48      0.56     1.38     3.63 1.00     4459
##                        Tail_ESS
## Intercept                  2924
## high_debt_versionfalse     3101
## 
## Samples were drawn using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Summary

summary(variable_names0.all.exp)

##  Family: binomial 
##   Links: mu = logit 
## Formula: var_names_new_good | trials(var_names_new_all) ~ 1 + high_debt_version + work_experience_programming.s + (1 | session) 
##    Data: as.data.frame(d.completed) (Number of observations: 51) 
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup samples = 4000
## 
## Group-Level Effects: 
## ~session (Number of levels: 29) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.76      0.57     0.81     3.07 1.00     1365     1777
## 
## Population-Level Effects: 
##                               Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept                         1.53      0.49     0.68     2.56 1.00
## high_debt_versionfalse            2.50      0.57     1.40     3.66 1.00
## work_experience_programming.s     0.15      0.47    -0.74     1.11 1.00
##                               Bulk_ESS Tail_ESS
## Intercept                         1902     2602
## high_debt_versionfalse            3610     2859
## work_experience_programming.s     2396     2518
## 
## Samples were drawn using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Random effects

ranef(variable_names0.all.exp)

## $session
## , , Intercept
## 
##                            Estimate Est.Error       Q2.5         Q97.5
## 6033c6fc5af2c702367b3a93 -1.4182361 1.1827451 -3.9014715  0.7405075250
## 6033d69a5af2c702367b3a95  1.0248475 1.4662706 -1.4678295  4.3656542500
## 6033d90a5af2c702367b3a96  1.3181878 1.4271892 -0.9734192  4.5846872500
## 6034fc165af2c702367b3a98 -1.3412419 0.6487407 -2.6612825 -0.0874654975
## 603500725af2c702367b3a99 -1.4686652 1.0913363 -3.6888770  0.5774463500
## 603f84f15af2c702367b3a9b  0.2668357 1.6400445 -2.8219980  3.7210642500
## 603f97625af2c702367b3a9d  1.3115338 1.3942632 -0.9248167  4.4947100000
## 603fd5d95af2c702367b3a9e -1.4897272 1.0749163 -3.7007410  0.5424600250
## 60409b7b5af2c702367b3a9f  1.2703161 1.4355589 -1.0773738  4.5062062500
## 604b82b5a7718fbed181b336 -0.8523828 0.8496030 -2.5182638  0.7348042750
## 604f1239a7718fbed181b33f  0.9114816 1.4889058 -1.5963553  4.3514157500
## 6050c1bf856f36729d2e5218 -1.9168515 1.0339995 -4.0199970 -0.0009028132
## 6050e1e7856f36729d2e5219  1.2747172 1.4296471 -1.0629927  4.6702740000
## 6055fdc6856f36729d2e521b  1.0303782 1.4959962 -1.5193685  4.3312645000
## 60579f2a856f36729d2e521e  0.2855757 1.6437444 -2.7615500  3.7951775000
## 60589862856f36729d2e521f  0.9694355 1.5701748 -1.7895887  4.4170072500
## 605a30a7856f36729d2e5221  0.1449444 1.7374905 -3.1083622  3.8912440000
## 605afa3a856f36729d2e5222 -1.8136133 1.2904502 -4.5523393  0.4529618500
## 605c8bc6856f36729d2e5223 -0.9854226 1.0173308 -3.0414090  0.9667453250
## 605f3f2d856f36729d2e5224  0.9172891 1.6122785 -2.1206710  4.4149135000
## 605f46c3856f36729d2e5225 -1.5721425 0.8818168 -3.3500108  0.0843726225
## 60605337856f36729d2e5226  1.0181315 1.4778241 -1.4552510  4.3759702500
## 60609ae6856f36729d2e5228  1.2786818 1.4149702 -0.9782539  4.5644302500
## 6061ce91856f36729d2e522e  1.3037518 1.4168388 -1.0236575  4.6591297500
## 6061f106856f36729d2e5231 -1.4808466 1.0753831 -3.5911405  0.5323328000
## 60672faa856f36729d2e523c  0.2831757 1.6193232 -2.6897402  3.6969037500
## 6068ea9f856f36729d2e523e  1.5953833 1.3507665 -0.4696562  4.6847365000
## 606db69d856f36729d2e5243  0.4684324 1.5947690 -2.4460730  4.0236922500
## 6075ab05856f36729d2e5247  1.3106881 1.4807536 -1.0039080  4.7142510000

Sampling plots

plot(variable_names0.all.exp, ask = FALSE)

Posterior predictive check

pp_check(variable_names0.all.exp, nsamples = 200, type = "bars")

Loo comparison

loo(
  variable_names0.all,
  variable_names0.all.exp
)

## Output of model 'variable_names0.all':
## 
## Computed from 4000 by 51 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -38.6  6.3
## p_loo        15.0  2.8
## looic        77.2 12.5
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     24    47.1%   1056      
##  (0.5, 0.7]   (ok)       17    33.3%   217       
##    (0.7, 1]   (bad)      10    19.6%   82        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## Output of model 'variable_names0.all.exp':
## 
## Computed from 4000 by 51 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo    -39.5  6.4
## p_loo        16.3  3.0
## looic        79.1 12.9
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     22    43.1%   1097      
##  (0.5, 0.7]   (ok)       15    29.4%   272       
##    (0.7, 1]   (bad)      14    27.5%   48        
##    (1, Inf)   (very bad)  0     0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.
## 
## Model comparisons:
##                         elpd_diff se_diff
## variable_names0.all      0.0       0.0   
## variable_names0.all.exp -0.9       0.4

Final model

• Fitting the model to all data point did not significantly damage the model and will be used as is a more fair representation of reality.
• Adding the experience predictors did not significantly damage the model and will be used as it provides useful insight.

This means that our final model, with all data points and experience predictors, is variable_names0.all.exp

Interpreting the model

To begin interpreting the model we look at how it’s parameters were estimated. As our research is focused on how the outcome of the model is effected we will mainly analyze the \(\beta\) parameters.

\(\beta\) parameters

mcmc_areas(variable_names0.all.exp, pars = c("b_high_debt_versionfalse", "b_work_experience_programming.s"), prob = 0.95) + scale_y_discrete() +
  scale_y_discrete(labels=c("High debt version: false", "Professional programming experience")) +
  ggtitle("Beta parameters densities in time model", subtitle = "Shaded region marks 95% of the density. Line marks the median")

Effects sizes

We start by extracting posterior samples

scale_programming_experience <- function(x) {
  (x - mean(d.completed$work_experience_programming))/ sd(d.completed$work_experience_programming)
}
unscale_programming_experience <- function(x) {
  x * sd(d.completed$work_experience_programming) + mean(d.completed$work_experience_programming)
}

post_settings <- expand.grid(
  high_debt_version = c("false", "true"),
  session = NA,
  var_names_new_all = 1000,
  work_experience_programming.s = sapply(c(0, 3, 10, 25, 40), scale_programming_experience)
)

post <- posterior_predict(variable_names0.all.exp, newdata = post_settings) %>%
  melt(value.name = "estimate", varnames = c("sample_number", "settings_id")) %>%
  left_join(
    rowid_to_column(post_settings, var= "settings_id"),
    by = "settings_id"
  ) %>%
  mutate(work_experience_programming = unscale_programming_experience(work_experience_programming.s)) %>%
  select(
    estimate,
    high_debt_version,
    work_experience_programming
  )%>%
  mutate(estimate = estimate/1000)

ggplot(post %>% filter(work_experience_programming == 10), aes(x=estimate, fill = high_debt_version)) +
  geom_density(alpha = 0.5) +
  scale_fill_manual(
    name = "Debt version",
    labels = c("Low debt", "High debt"),
    values = c("lightblue", "darkblue")
  ) +
  facet_grid(rows = vars(work_experience_programming)) +
  labs(
    title = "Rate of good variable naming",
    x = "Rate",
    y = "Density"
  )

ggplot(post, aes(x=estimate, fill = high_debt_version)) +
  geom_density(alpha = 0.5) +
  scale_fill_manual(
    name = "Debt version",
    labels = c("Low debt", "High debt"),
    values = c("lightblue", "darkblue")
  ) +
  facet_grid(rows = vars(work_experience_programming)) +
  labs(
    title = "Rate of good variable naming",
    x = "Rate",
    y = "Density"
  )

scale_programming_experience <- function(x) {
  (x - mean(d.completed$work_experience_programming))/ sd(d.completed$work_experience_programming)
}
unscale_programming_experience <- function(x) {
  x * sd(d.completed$work_experience_programming) + mean(d.completed$work_experience_programming)
}

post_settings <- expand.grid(
  high_debt_version = c("false", "true"),
  session = NA,
  var_names_new_all = 10,
  work_experience_programming.s = sapply(c(10), scale_programming_experience)
)

post <- posterior_predict(variable_names0.all.exp, newdata = post_settings) %>%
  melt(value.name = "estimate", varnames = c("sample_number", "settings_id")) %>%
  left_join(
    rowid_to_column(post_settings, var= "settings_id"),
    by = "settings_id"
  ) %>%
  mutate(work_experience_programming = unscale_programming_experience(work_experience_programming.s)) %>%
  select(
    estimate,
    high_debt_version,
    work_experience_programming
  )

levels(post$high_debt_version) <- c("Low debt version", "High debt version")

ggplot(post, aes(x=estimate, fill = high_debt_version)) +
  geom_bar() +
  facet_grid(rows = vars(high_debt_version)) +
  scale_fill_manual(
    name = "Debt version",
    labels = c("Low debt version", "High debt version"),
    values = c("lightblue", "darkblue")
  ) +
  labs(
    title = "Variable naming (10 named variables)",
    x = "Number of good variable names",
    y = "Rate of occurrence"
  ) +
  theme_minimal() +
  scale_x_continuous(breaks = c(0,1,2,3,4,5,6,7,8,9,10), labels = c(0,1,2,3,4,5,6,7,8,9,10)) +
  scale_y_continuous(limits = NULL, breaks = c(500,1000,1500,2000,2500), labels = c("10%","20%","30%","40%","50%")) + theme(legend.position = "hidden")

We can also plot the difference between good variable names for the high debt version and the low debt version.